Let denote the set of all matrices over a semiring S. For , zero-term rank of A is the minimal number of lines (rows or columns) needed to cover all zero entries in A. In [5], the authors obtained that a linear operator on preserves zero-term rank if and only if it preserves zero-term ranks 0 and 1. In this paper, we obtain new characterizations of linear operators on that preserve zero-term rank. Consequently we obtain that a linear operator on preserves zero-term rank if and only if it preserves two consecutive zero-term ranks k and k + 1, where if and only if it strongly preserves zero-term rank h, where .